10 pts 3A ten to A 25 question TrueFalse Statistics final is

(10 pts.] 3A ten to A 25 question True-False Statistics final is given and Sam Plespace has forgot study for the final??!!l. So. Sam decides to guess at all of the answers. If welet X = # questions that Sam got \"right\", then X is a binomial random variable Identify the compute and . Interpret in this situation. (a) n, p, and q for the distribution and use the shortcut formulas to (b) Compute the probability that he will get at least 15 correct (a 60%) ?

Solution

Here,

n = number of items = 25
p = probability of correct = 1/2 (As it is true or false)
q = 1 - p = 0.5

Thus,

u = n p = 12.5
sigma = sqrt(n p q) = 2.5

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b.
Using normal approximation,

P(at least 15 correct) = P(x > 14.5)

Thus We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    14.5      
u = mean =    12.5      
n = sample size =    1      
s = standard deviation =    2.5      
          
Thus,          
          
z =    0.8      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.8   ) =    0.211855399 [ANSWER]